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An important episode for my understanding of conduction problems arose from a paper by Kretschmann, ... who attacked the then accepted theory of cond… - Rudolf Peierls
" "An important episode for my understanding of conduction problems arose from a paper by Kretschmann, ... who attacked the then accepted theory of conductivity and claimed that the basis of the papers by Bloch and others was quite wrong. He had a number of objections which were mostly not very well conceived, but he claimed, in particular, that in the usual derivation of the Boltzmann equation one had made unjustified use of perturbation theory. In trying to defend the theory I therefore set out to prove that perturbation theory was in order, and to my amazement I found that this was very questionable, if not exactly for the reasons given by Kretschmann. It appeared that the usual application of Fermi's 'golden rule' depended on the inequality ħ/τ ≪ kT,
where τ is the collision time. This was not satisfied for many metals. Indeed Landau's dimensional analysis made them comparable. ...
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About Rudolf Peierls
Sir Rudolf Ernst Peierls (5 June 1907 – 19 September 1995) was a German-born British physicist, known as one of the pioneers of quantum mechanics. His honours include the Max Planck Medal in 1963, a British knighthood in 1968, the Copley Medal in 1986, and the Dirac Medal and Prize in 1991. Peierls played a major role in Tube Alloys, Britain's nuclear weapon programme, as well as the subsequent Manhattan Project, the combined Allied nuclear bomb programme.
Also Known As
Native Name:
Rudolf Ernst Peierls
Alternative Names:
R.E. Peierls
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Sir Rudolf Ernst Peierls
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Sir Rudolph Ernst Peierls
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Additional quotes by Rudolf Peierls
Any theoretical physicist has met, in his introduction to the subject, the simplest examples of Schrödinger's equation, including the harmonic oscillator. In demonstrating its solution, it is usually shown that for energies satisfying the usual quantum condition, E = (n + ½)ħω (1.1.1)
where n is a non-negative integer and ω the frequency, the equation has a solution satisfying the correct boundary conditions. It is equally important to know that these are the only solutions, i.e., that for an energy not equal to (1.1.1) no admissible solution exists. This negative statement is not usually proved in elementary treatments, or else it is deduced from quite elaborate discussions of the convergence and behavior of a certain infinite series. It is therefore surprising to find that the result can be seen without any complicated algebra.
1.4 Types of binding
... The most important types of force are as follows:
(a) Electrostatic forces. In an ionic crystal the attraction is mainly due to the Coulomb interaction between point charges. This is particularly amenable to calculation, and a great deal of work has been done on it. The force is a 'two-body' force, i.e. the interaction between two given ions is independent of the positions of any other ions that may be present. ...
(b) Van der Waals forces. This name describes the effect that a neutral and isotropic atom can acquire a polarization under the influence of an electric field, and even two neutral isotropic atoms will induce small dipole moments in each other, due to the fluctuating moments which they possess because of the existence of virtual excited states. ...
(c) Homopolar binding. These are forces like those effective in homopolar molecules, and we know they are due to the exchange of electrons between the atoms. In molecular crystals (H<sub>2</sub>, Cl<sub>2</sub>, etc.) these bonds can easily be localized and we can start from a description of the molecular by the methods of quantum chemistry and then add the relatively weak forces between different molecules. In other cases, however, such as diamond or graphite, each atom shares some valence electrons with each of its neighbors, and it is therefore not possible to single out any given groups of atoms that may be regarded as chemically saturated. The quantitative discussion of such forces is not easy. ...
(d) Overlap. If two atoms approach so closely that their electron shells overlap, then there is a strong repulsive force between them. ...
(e) Metallic bond. ... it is worth noting that in the case of a metal the presence and motion of the conduction electrons is an important factor in holding the crystal together and in determining its structure.
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